sage: H = DirichletGroup(2601)
pari: g = idealstar(,2601,2)
Character group
| sage: G.order()
pari: g.no
| ||
| Order | = | 1632 |
| sage: H.invariants()
pari: g.cyc
| ||
| Structure | = | \(C_{2}\times C_{816}\) |
| sage: H.gens()
pari: g.gen
| ||
| Generators | = | $\chi_{2601}(290,\cdot)$, $\chi_{2601}(2026,\cdot)$ |
First 32 of 1632 characters
Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.
| Character | Orbit | Order | Primitive | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{2601}(1,\cdot)\) | 2601.a | 1 | no | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(\chi_{2601}(2,\cdot)\) | 2601.bl | 408 | yes | \(-1\) | \(1\) | \(e\left(\frac{181}{204}\right)\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{325}{408}\right)\) | \(e\left(\frac{383}{408}\right)\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{95}{408}\right)\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{337}{408}\right)\) | \(e\left(\frac{28}{51}\right)\) |
| \(\chi_{2601}(4,\cdot)\) | 2601.bg | 204 | yes | \(1\) | \(1\) | \(e\left(\frac{79}{102}\right)\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{179}{204}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{95}{204}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{5}{51}\right)\) |
| \(\chi_{2601}(5,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{325}{408}\right)\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{787}{816}\right)\) | \(e\left(\frac{677}{816}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{161}{816}\right)\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{511}{816}\right)\) | \(e\left(\frac{19}{102}\right)\) |
| \(\chi_{2601}(7,\cdot)\) | 2601.bm | 816 | yes | \(-1\) | \(1\) | \(e\left(\frac{383}{408}\right)\) | \(e\left(\frac{179}{204}\right)\) | \(e\left(\frac{677}{816}\right)\) | \(e\left(\frac{811}{816}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{209}{272}\right)\) | \(e\left(\frac{631}{816}\right)\) | \(e\left(\frac{5}{204}\right)\) | \(e\left(\frac{761}{816}\right)\) | \(e\left(\frac{77}{102}\right)\) |
| \(\chi_{2601}(8,\cdot)\) | 2601.bf | 136 | no | \(-1\) | \(1\) | \(e\left(\frac{45}{68}\right)\) | \(e\left(\frac{11}{34}\right)\) | \(e\left(\frac{53}{136}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{95}{136}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{11}{17}\right)\) |
| \(\chi_{2601}(10,\cdot)\) | 2601.bi | 272 | no | \(-1\) | \(1\) | \(e\left(\frac{93}{136}\right)\) | \(e\left(\frac{25}{68}\right)\) | \(e\left(\frac{207}{272}\right)\) | \(e\left(\frac{209}{272}\right)\) | \(e\left(\frac{7}{136}\right)\) | \(e\left(\frac{121}{272}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{123}{272}\right)\) | \(e\left(\frac{25}{34}\right)\) |
| \(\chi_{2601}(11,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{95}{408}\right)\) | \(e\left(\frac{95}{204}\right)\) | \(e\left(\frac{161}{816}\right)\) | \(e\left(\frac{631}{816}\right)\) | \(e\left(\frac{95}{136}\right)\) | \(e\left(\frac{117}{272}\right)\) | \(e\left(\frac{91}{816}\right)\) | \(e\left(\frac{185}{204}\right)\) | \(e\left(\frac{5}{816}\right)\) | \(e\left(\frac{95}{102}\right)\) |
| \(\chi_{2601}(13,\cdot)\) | 2601.bg | 204 | yes | \(1\) | \(1\) | \(e\left(\frac{25}{102}\right)\) | \(e\left(\frac{25}{51}\right)\) | \(e\left(\frac{139}{204}\right)\) | \(e\left(\frac{5}{204}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{63}{68}\right)\) | \(e\left(\frac{185}{204}\right)\) | \(e\left(\frac{46}{51}\right)\) | \(e\left(\frac{55}{204}\right)\) | \(e\left(\frac{50}{51}\right)\) |
| \(\chi_{2601}(14,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{337}{408}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{511}{816}\right)\) | \(e\left(\frac{761}{816}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{123}{272}\right)\) | \(e\left(\frac{5}{816}\right)\) | \(e\left(\frac{55}{204}\right)\) | \(e\left(\frac{619}{816}\right)\) | \(e\left(\frac{31}{102}\right)\) |
| \(\chi_{2601}(16,\cdot)\) | 2601.bd | 102 | yes | \(1\) | \(1\) | \(e\left(\frac{28}{51}\right)\) | \(e\left(\frac{5}{51}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{11}{17}\right)\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{95}{102}\right)\) | \(e\left(\frac{50}{51}\right)\) | \(e\left(\frac{31}{102}\right)\) | \(e\left(\frac{10}{51}\right)\) |
| \(\chi_{2601}(19,\cdot)\) | 2601.be | 136 | no | \(1\) | \(1\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{107}{136}\right)\) | \(e\left(\frac{133}{136}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{77}{136}\right)\) | \(e\left(\frac{25}{136}\right)\) | \(e\left(\frac{3}{34}\right)\) | \(e\left(\frac{103}{136}\right)\) | \(e\left(\frac{2}{17}\right)\) |
| \(\chi_{2601}(20,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{233}{408}\right)\) | \(e\left(\frac{29}{204}\right)\) | \(e\left(\frac{455}{816}\right)\) | \(e\left(\frac{577}{816}\right)\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{35}{272}\right)\) | \(e\left(\frac{541}{816}\right)\) | \(e\left(\frac{35}{204}\right)\) | \(e\left(\frac{227}{816}\right)\) | \(e\left(\frac{29}{102}\right)\) |
| \(\chi_{2601}(22,\cdot)\) | 2601.bm | 816 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{408}\right)\) | \(e\left(\frac{49}{204}\right)\) | \(e\left(\frac{811}{816}\right)\) | \(e\left(\frac{581}{816}\right)\) | \(e\left(\frac{49}{136}\right)\) | \(e\left(\frac{31}{272}\right)\) | \(e\left(\frac{281}{816}\right)\) | \(e\left(\frac{31}{204}\right)\) | \(e\left(\frac{679}{816}\right)\) | \(e\left(\frac{49}{102}\right)\) |
| \(\chi_{2601}(23,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{247}{408}\right)\) | \(e\left(\frac{43}{204}\right)\) | \(e\left(\frac{745}{816}\right)\) | \(e\left(\frac{335}{816}\right)\) | \(e\left(\frac{111}{136}\right)\) | \(e\left(\frac{141}{272}\right)\) | \(e\left(\frac{563}{816}\right)\) | \(e\left(\frac{73}{204}\right)\) | \(e\left(\frac{13}{816}\right)\) | \(e\left(\frac{43}{102}\right)\) |
| \(\chi_{2601}(25,\cdot)\) | 2601.bk | 408 | yes | \(1\) | \(1\) | \(e\left(\frac{121}{204}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{379}{408}\right)\) | \(e\left(\frac{269}{408}\right)\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{161}{408}\right)\) | \(e\left(\frac{37}{102}\right)\) | \(e\left(\frac{103}{408}\right)\) | \(e\left(\frac{19}{51}\right)\) |
| \(\chi_{2601}(26,\cdot)\) | 2601.bf | 136 | no | \(-1\) | \(1\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{131}{136}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{83}{136}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{5}{34}\right)\) | \(e\left(\frac{13}{136}\right)\) | \(e\left(\frac{9}{17}\right)\) |
| \(\chi_{2601}(28,\cdot)\) | 2601.bi | 272 | no | \(-1\) | \(1\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{29}{68}\right)\) | \(e\left(\frac{115}{272}\right)\) | \(e\left(\frac{237}{272}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{37}{272}\right)\) | \(e\left(\frac{65}{272}\right)\) | \(e\left(\frac{35}{68}\right)\) | \(e\left(\frac{159}{272}\right)\) | \(e\left(\frac{29}{34}\right)\) |
| \(\chi_{2601}(29,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{197}{408}\right)\) | \(e\left(\frac{197}{204}\right)\) | \(e\left(\frac{59}{816}\right)\) | \(e\left(\frac{733}{816}\right)\) | \(e\left(\frac{61}{136}\right)\) | \(e\left(\frac{151}{272}\right)\) | \(e\left(\frac{601}{816}\right)\) | \(e\left(\frac{83}{204}\right)\) | \(e\left(\frac{311}{816}\right)\) | \(e\left(\frac{95}{102}\right)\) |
| \(\chi_{2601}(31,\cdot)\) | 2601.bm | 816 | yes | \(-1\) | \(1\) | \(e\left(\frac{253}{408}\right)\) | \(e\left(\frac{49}{204}\right)\) | \(e\left(\frac{199}{816}\right)\) | \(e\left(\frac{377}{816}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{235}{272}\right)\) | \(e\left(\frac{77}{816}\right)\) | \(e\left(\frac{31}{204}\right)\) | \(e\left(\frac{67}{816}\right)\) | \(e\left(\frac{49}{102}\right)\) |
| \(\chi_{2601}(32,\cdot)\) | 2601.bl | 408 | yes | \(-1\) | \(1\) | \(e\left(\frac{89}{204}\right)\) | \(e\left(\frac{89}{102}\right)\) | \(e\left(\frac{401}{408}\right)\) | \(e\left(\frac{283}{408}\right)\) | \(e\left(\frac{21}{68}\right)\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{67}{408}\right)\) | \(e\left(\frac{23}{102}\right)\) | \(e\left(\frac{53}{408}\right)\) | \(e\left(\frac{38}{51}\right)\) |
| \(\chi_{2601}(35,\cdot)\) | 2601.v | 34 | no | \(-1\) | \(1\) | \(e\left(\frac{25}{34}\right)\) | \(e\left(\frac{8}{17}\right)\) | \(e\left(\frac{27}{34}\right)\) | \(e\left(\frac{14}{17}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{9}{17}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{12}{17}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{16}{17}\right)\) |
| \(\chi_{2601}(37,\cdot)\) | 2601.bi | 272 | no | \(-1\) | \(1\) | \(e\left(\frac{15}{136}\right)\) | \(e\left(\frac{15}{68}\right)\) | \(e\left(\frac{165}{272}\right)\) | \(e\left(\frac{139}{272}\right)\) | \(e\left(\frac{45}{136}\right)\) | \(e\left(\frac{195}{272}\right)\) | \(e\left(\frac{247}{272}\right)\) | \(e\left(\frac{65}{68}\right)\) | \(e\left(\frac{169}{272}\right)\) | \(e\left(\frac{15}{34}\right)\) |
| \(\chi_{2601}(38,\cdot)\) | 2601.m | 12 | no | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(1\) | \(i\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) |
| \(\chi_{2601}(40,\cdot)\) | 2601.x | 48 | no | \(-1\) | \(1\) | \(e\left(\frac{11}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{31}{48}\right)\) | \(e\left(\frac{3}{8}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{5}{6}\right)\) |
| \(\chi_{2601}(41,\cdot)\) | 2601.bn | 816 | yes | \(1\) | \(1\) | \(e\left(\frac{115}{408}\right)\) | \(e\left(\frac{115}{204}\right)\) | \(e\left(\frac{109}{816}\right)\) | \(e\left(\frac{635}{816}\right)\) | \(e\left(\frac{115}{136}\right)\) | \(e\left(\frac{113}{272}\right)\) | \(e\left(\frac{239}{816}\right)\) | \(e\left(\frac{181}{204}\right)\) | \(e\left(\frac{49}{816}\right)\) | \(e\left(\frac{13}{102}\right)\) |
| \(\chi_{2601}(43,\cdot)\) | 2601.bk | 408 | yes | \(1\) | \(1\) | \(e\left(\frac{109}{204}\right)\) | \(e\left(\frac{7}{102}\right)\) | \(e\left(\frac{247}{408}\right)\) | \(e\left(\frac{185}{408}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{19}{136}\right)\) | \(e\left(\frac{317}{408}\right)\) | \(e\left(\frac{19}{102}\right)\) | \(e\left(\frac{403}{408}\right)\) | \(e\left(\frac{7}{51}\right)\) |
| \(\chi_{2601}(44,\cdot)\) | 2601.bj | 272 | no | \(1\) | \(1\) | \(e\left(\frac{1}{136}\right)\) | \(e\left(\frac{1}{68}\right)\) | \(e\left(\frac{215}{272}\right)\) | \(e\left(\frac{177}{272}\right)\) | \(e\left(\frac{3}{136}\right)\) | \(e\left(\frac{217}{272}\right)\) | \(e\left(\frac{157}{272}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{179}{272}\right)\) | \(e\left(\frac{1}{34}\right)\) |
| \(\chi_{2601}(46,\cdot)\) | 2601.bi | 272 | no | \(-1\) | \(1\) | \(e\left(\frac{67}{136}\right)\) | \(e\left(\frac{67}{68}\right)\) | \(e\left(\frac{193}{272}\right)\) | \(e\left(\frac{95}{272}\right)\) | \(e\left(\frac{65}{136}\right)\) | \(e\left(\frac{55}{272}\right)\) | \(e\left(\frac{251}{272}\right)\) | \(e\left(\frac{41}{68}\right)\) | \(e\left(\frac{229}{272}\right)\) | \(e\left(\frac{33}{34}\right)\) |
| \(\chi_{2601}(47,\cdot)\) | 2601.bh | 204 | yes | \(-1\) | \(1\) | \(e\left(\frac{1}{51}\right)\) | \(e\left(\frac{2}{51}\right)\) | \(e\left(\frac{5}{204}\right)\) | \(e\left(\frac{133}{204}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{127}{204}\right)\) | \(e\left(\frac{20}{51}\right)\) | \(e\left(\frac{137}{204}\right)\) | \(e\left(\frac{4}{51}\right)\) |
| \(\chi_{2601}(49,\cdot)\) | 2601.bk | 408 | yes | \(1\) | \(1\) | \(e\left(\frac{179}{204}\right)\) | \(e\left(\frac{77}{102}\right)\) | \(e\left(\frac{269}{408}\right)\) | \(e\left(\frac{403}{408}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{73}{136}\right)\) | \(e\left(\frac{223}{408}\right)\) | \(e\left(\frac{5}{102}\right)\) | \(e\left(\frac{353}{408}\right)\) | \(e\left(\frac{26}{51}\right)\) |
| \(\chi_{2601}(50,\cdot)\) | 2601.bc | 102 | yes | \(-1\) | \(1\) | \(e\left(\frac{49}{102}\right)\) | \(e\left(\frac{49}{51}\right)\) | \(e\left(\frac{37}{51}\right)\) | \(e\left(\frac{61}{102}\right)\) | \(e\left(\frac{15}{34}\right)\) | \(e\left(\frac{7}{34}\right)\) | \(e\left(\frac{32}{51}\right)\) | \(e\left(\frac{31}{51}\right)\) | \(e\left(\frac{4}{51}\right)\) | \(e\left(\frac{47}{51}\right)\) |